Effectiveness of Spatial and Fourier Layer: To further demonstrate the strong learning ability of SFL, we introduce self-attention and transformer to replace the SFL. The results are shown in Table. REF . The running-time is an average time, which is calculated on 100 images of \(512\times 512\) . The CLGNet\(_{non}\)  is the CLGNet without SFL, self-attention, and Transformer, which only learn the local information. CLGNet\(_{SA}\)  is the CLGNet with self-attention and CLGNet\(_{Tran}\)  is the CLGNet with transformer. For CLGNet\(_{SA}\) , we only add the self-attention in the end of SFRIR, since self-attention is time-consuming and memory-consuming. In addition, for CLGNet\(_{Tran}\) , we use the Residual Swin Transformer Block proposed (RSTB) in SwinIR [1]} to replace the SFRIR. For a fair comparison, we try to keep the parameters of all models consistent. From Table. REF , our proposed CLGNet, CLGNet\(_{SA}\) , and CLGNet\(_{Tran}\)  outperform CLGNet\(_{non}\)  in NMSE, PSNR, and SSIM, which shows that learning global information is essential for MRI reconstruction. Moreover, compared with CLGNet\(_{SA}\)  and CLGNet\(_{Tran}\) , our proposed CLGNet achieves significant performance improvements and the running-times of our proposed CLGNet is also less than CLGNet\(_{SA}\)  and CLGNet\(_{Tran}\) , which indicates that SFL can learn global information more effectively than self-attention and Transformer in less time. Meanwhile, compared CLGNet\(_{non}\) , the running-time and Flops of the proposed CLGNet only increase a little, which indicates that SFL based on FFT only slightly increases calculation and running-time compared to the convolution layer. Hence, from Table. REF , it is observed that SFL has a strong learning ability and only adds a little running-time and calculation. In addition, Fig. REF  illustrates the results of different methods. It is obvious that the proposed CLGNet can reconstruct high-quality MR images than other CLGNet\(_{SA}\)  and CLGNet\(_{Tran}\) , which indicates that SFL can learn global information more effectively.
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